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DNA Expressions

Rudy van Vliet. Leiden Institute of Advanced Computer Science Leiden University. DNA Expressions. A formal notation for DNA molecules. LIACS PhD talk September 15, 2004. A. C. G. T. A. A. C. T. A. G. T. C. G. A. T. C. G. A. T. T. Building blocks. A. A. C. C. A. A.

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DNA Expressions

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  1. Rudy van Vliet Leiden Institute of Advanced Computer Science Leiden University DNA Expressions A formal notation for DNA molecules LIACS PhD talk September 15, 2004

  2. A C G T A A C T A G T C G A T C G A T T Building blocks A A C C A A T T G G C C A A T T T T G A T C G A T C A G C T A A T T G G T T A A C C G G T T A A Complementarity Strand s Perfect double stranded DNA C A G T G T C A Upper strand Lower strand Same molecule DNA Genetic information

  3. DNA and computer science Evolutionary algorithms DNA computing theory - splicing practice - Hamiltonian path problem

  4. A C A T G C A T T G T A C G T A A C A T G C A T Secondary structure: Hairpin loop: T G A A C C G C G G C A T A C A A T T T G T A C G T A A Why notation? Perfect double stranded molecule:

  5. Why notation?

  6. A C A T G C A T T G T A C G T A A C A T G T A G C T A A T C G T G T A C A T G T G C A C A T G C T G T C G T A Gaps and nicks no gaps, no nicks gaps, no nicks gaps, lower nicks no gaps, upper nick gap, upper nick, lower nick

  7. A G T C ………  ……… C A T G T G C ………       T T C C AT AT      G G G T A T C     Abstract DNA molecules bases + operators DNA expressions minimal DNA expressions

  8. A G T C ………  ……… C A T G T G C ………       T T C C AT AT      G G G T A T C     Abstract (2) DNA molecules bases + operators DNA expressions normal form DNA expression

  9. N-words ACATGCAT

  10. AT lower nicks may appear removes upper nicks creates upper strands connects upper strands of arguments    A A C G A C T G C T T C T G C G G C A T A G  DNAexpressions

  11. AT upper nicks may appear removes lower nicks creates lower strands connects lower strands of arguments T T   A C G C T A C A T C G T C A G T T G C A A T A T C C G C G T G A T T A A C G G C T G G A C G  DNAexpressions 

  12. A C A T G C A T AT T G T A C G T A connects new nucleotides to neighbours complements argument T T T   T C A T C A G G T A C C C C T A G C C G T A T G A T A C C A T C T A G G C T G G C G G G T A G A A G C T T A G G C A C T  DNAexpressions  C 

  13. A A C C A A T T G G C C A A T T AT T T G G T T A A C C G G T T A A T T T           A A C C T T T C C A T A G C T A A C T G A C G T A T C C G C G A T C  T G G G C A G C G A A G C T T G A T G G T A G G C C   DNAexpressions  C T C AT G C A T

  14. A A C C A A T T G G C C  A A T T AT T T G G T T A A C C G G T T A A  T T   T         T AT C A C T G G A C C T A C T G C C A C T T A G C T C C T G A T A T A A  G G T C A A G C G T G C T A A G C C G G G T G G T A DNAexpressions C  C G C A T

  15. A A C C A A T T G G C C A A T T AT T T G G T T A A C C G G T T A A T T T           A A C C T T T C C A T A G C T A A C T G A C G T A T C C G C G A T C  T G G G C A G C G A A G C T T G A T G G T A G G C C   DNAexpressions  C T C AT G C A T

  16. A C A T G C A T T G T A C G T A A C A T G T A G C T A A T C G T G T A C A T G T G C A C A T G C T G T C G T A Expressible DNA molecules A DNA molecule is expressible, if and only if it contains nicks in at most one strand.     

  17. A C A T G C A T T G T A C G T A ACATGC AT              Equivalent DNA expressions T C AT G C A T

  18. Introduction of DNA expressions For each expressible DNA molecule, Number of minimal DNA expressions Characterization of minimal DNA expressions Normal form      www.liacs.nl/home/rvvliet/mindnaexpr.html (in terms of Catalan numbers) Conclusions we can construct the minimal DNA expressions More info:

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